The invention relates to a method and apparatus for determining the resonant frequencies of vibration of rotating blades, particularly those in turbo-machines.
During operation of a turbo-machine, its rotating blades vibrate at frequencies which coincide with integer multiples (harmonics) of the assembly rotation frequency (the frequency of rotation of the rotor on which the blades are mounted) This vibration is referred to as synchronous vibration, or the synchronous response of the blades. The synchronous response can be characterised by its amplitude and its frequency, with the frequency always being equal to the assembly rotation frequency multiplied by an integer known as the order of the response.
Turbine blades have a tendency to vibrate at large amplitudes at certain natural or resonant frequencies. These resonant frequencies would usually be associated with a particular natural movement of the blade or combination of movements of the blade. For example, one resonant frequency might represent vibration of the blade along the rotational axis of the turbine and another might represent vibration perpendicular to the rotational axis of the turbine.
If the assembly rotation frequency has harmonics which coincide with any of the resonant frequencies of vibration of the turbine blades, synchronous vibrations will occur at these resonant frequencies. Thus, the amplitudes of the synchronous vibrations will be high.
When the amplitude of vibration of the blades exceeds a certain level, excessive stresses are generated in the blades, which suffer from damage and may even fracture. Thus, it is very important to know what are the resonant frequencies of vibration of the blades and prevent vibration taking place at these frequencies.
It is known to obtain information about the amplitude and frequency of vibration of rotating blades by recording the time at which a blade passes a stationary probe. This time is compared with the time at which the blade would have passed the probe if it were undergoing no vibration. This is termed the "expected arrival time" and can be calculated from the rotational position of the particular blade on the rotor in conjunction with a "once per revolution" or "OPR" signal which provides information about the position of the rotor. This OPR signal is derived from the time at which an indicator on the rotor passes a reference sensor, and its use is well known in the art.
The difference between the expected arrival time and the actual arrival time can be multiplied by the turbine blade tip velocity to give the displacement of the blade from its expected position. Data from a plurality of sensors can be processed to obtain the amplitudes and frequencies of vibration of the blades.
It is known that synchronous vibrations of order E can be characterised using 2.times.E+3 near-equispaced sensors, each measuring times of blade tip passage. Equispaced sensors provide uniformly sampled data which can be analysed using standard frequency domain processing techniques. A tip timing system using 50 sensors has been demonstrated (Endoh, M; Matsuda, Y; and Matsuki, M: "Noncontact Measurement of Rotating Blade Vibrations", presented at International Gas Turbine Congress 1983). However as the number of measurement points increases, probe installation becomes difficult and data acquisition hardware costs prohibitive. It is therefore highly desirable to reduce the number of sensors required to provide amplitude and frequency information.
The maximum synchronous response amplitude can be derived using measurements taken from a single sensor (Zablotskiy,I. Ye. and Korostelev, Yu. A., "Measurement of Resonance Vibrations of Turbine Blades with the ELURA Device", Energomashinostroneniye, pp 36-39, 1970). However, no response frequency information can be derived from this single sensor measurement.